4. e Fuzzy-Techniques-in-Object-Oriented-Databases 2011

International Journal of Scientific & Engineering Research, Volume 2, Issue 11, November-2011
ISSN 2229-5518

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A Survey of Fuzzy Techniques in Object Oriented
Databases
Praveen Kumar Shukla, Manuj Darbari, Vivek Kumar Singh, Surya Prakash Tripathi

Abstract—Exact information has become crucial part of the modern database applications and next generation information systems to
make them more human friendly. In order to deal with information inexactness, fuzzy techniques have been extensively integrated with different database models and theories. But, object oriented database systems are extremely capable to represent and manipulate the complex objects as well as complicated and uncertain relationship existing among them. They are also much suitable for engineering and
scientific applications, dealing with large data intensive applications. In this paper, a survey of different approaches regarding integration of
fuzzy techniques in object oriented databases has been sketched, under numerous categories of conceptual data modeling, querying, indexing etc.
Index Terms— Fuzzy Techniques, Inexact Information, ODMG (Object Data Management Group), FODMG (Fuzzy Object Data Management Group), FSM (Fuzzy Semantic Model), FOOD (Fuzzy Object Oriented Databases).

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1 INTRODUCTION

O

bject oriented databases are considered better than the
relational and other databases, due to increasing demand
of new approaches to deal with complex data , complex
relationship existing among such data and large data intensive
applications. These databases are much suitable for modern
database applications, like CAD/CAM (Computer Aided Design/Computer Aided Manufacturing), CASE (Computer
Aided Software Engineering), GIS (Geographical Information
Systems), Spatial Databases, Office Automation; Knowledge
based Systems, Hardware and Software Design, Network
Management, Multimedia databases, VLSI (Very Large Scale

Integrated) Design. In these applications, several types of information inexactness exist. Such incomplete and ill-defined
information has been accepted, represented and manipulated
with a certainty measure of acceptance using fuzzy techniques.
The integration of fuzzy techniques in databases makes
these systems to be closer with human activities. These may
include, dealing with different fuzzy concepts, like ‗almost all‘,
‗majority‘, ‗approximately‘, which include a certain vagueness
or uncertainty.
As far as the usability point of object oriented database systems is concerned, these are much suitable for scientific and

engineering applications, but not very much suitable for industrial and commercial applications. The complex imperfect
information has been represented, stored and retrieved in object oriented databases using fuzzy techniques. Complex object structures can be represented well in object oriented databases without fragmentation of aggregate data and also model
complex relationship among attributes. As far as the shortcomings are concerned in fuzzy object oriented database, it
shows lack of formal semantics and algebra for manipulation
and representation of knowledge as well as the inexact information data/information.
This paper has been organized into seven sections. In section 2, different types of information inexactness has been introduced. Section 3 briefly introduces the concept of fuzzy
logic. Different conceptual data modeling techniques has been
discussed in section 4. Several types of proposals, including
ODMG based framework, Graph based, Rough set based,
Fuzzy type based data models and mathematical fuzzy object
algebra, for fuzzy object oriented databases have been reviewed in section 5. Section 6 contains multiple issues regarding querying in fuzzy object oriented databases. Indexing in
fuzzy object oriented databases has been discussed in section
7.

2 INEXACTNESS IN INFORMATION

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 Praveen Kumar Shukla is pursuing Ph.D. in Compter Science from Gautam Buddh Technical University,Lucknow, India and he is also working as
a faculty in the department of Information Technology in Northern India

Engineering College,Lucknow,India.E-mail:
 Manuj Darbari is working as Associate Professor with the Department of
InfomationTechnology in Babu Banarsi Das National Institute of Technology and Management,Lucknow, India E-mail:
 Vivek Kumar Singh is currently working as Associate Professor in the
Department of InfomationTechnology in Babu Banarsi Das National Institute of Technology and Management, Lucknow, India.
 Surya Prakash Tripathi is working as Professor in Department of Compter
Science at Institute of Engineering & Technology, Lucknow, India,E-mail:


Several kinds of inexactness have been identified in real world
engineering and scientific data. These may be considered as:-1.
Imprecision 2. Vagueness 3. Uncertainty 4. Ambiguity 5. Inconsistency.

2.1 Imprecision
It is related to the content of values. A choice may be made
from set of values. For example, like the size of disk is in the
set {40 GB, 120GB, 180 GB}.
2.2 Uncertainty

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International Journal of Scientific & Engineering Research, Volume 2, Issue 11, November-2011
ISSN 2229-5518

In this case, we are not sure about the value of any attribute.
We can express our some belief to value to be true. For example, I am 95 % sure that a particular student has passed the
examination.

2.3 Ambiguity
Few elements of the models lack the complete semantics leading to several possible interpretations. For example, in a company salary of any employee may be monthly, daily or weekly.
2.4 Inconsistency
Values of any attribute which are different at different places
either in same or in different databases, leads to inconsistency
in data. For example, the salary of any employee is Rs. 10000
at one place and Rs. 12,000 at another place.
2.5 Fuzziness
We can say a value to be fuzzy, if its precise measurement is
obtained in principle. For example, somebody is tall, which is
not well defined. Other examples include: cold, warm, hot etc.
2.6 Vagueness
It is also related to the content of values, but the value of any
attribute is represented by linguistic variables. It is the subcategory of fuzziness. Those terms which have no measurement process are called vague quantities. For example, he is
uncomfortable with his tall height. Here, tall is a fuzzy term,
but uncomfortable is a vague term.
2.7 NULL Values
When a value is missing, how should this be indicated? A
missing value may exist, but be unknown, not exist at all or be
inapplicable. Several NULL markers have been used to
represent such type of situations.
2.8 Context dependence
Context is very important concept to make the data values
precise. For example, the value of term ‗high‘ is different for
‗high speed car‘ and a ‗high building‘.
Such type of information imprecision discussed above, may
be identified at different places in many information and database system applications. Decision making process in knowledge-intensive applications has various forms of inexactness
as well as different possible semantic implementations of data
are also integrated. Information in many non-traditional applications may be complex as well as uncertain, for example,
opinions and decisions in medical diagnosis, economic forecasting, whether forecasting. As far as natural language is concerned several modifiers (‗very‘, ‗more‘ or ‗less‘), and quantifiers (―many‖, ―few‖, ―most‖) are considered as the vague information.

3 INTRODUCTION TO FUZZY LOGIC
Fuzzy logic [1, 2] is considered as a mathematical soft computing tool to deal with inexact and subjective information. It
was first introduced by L. A. Zadeh in 1965.
Fuzzy set A can be defined over a universe of discourse U
can be defined as:

A  { A (u) / u : u U ,  A (u) [0,1]  }

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Here µA (u) is called the membership degree of element u to
the fuzzy set A and 0≤ µA (u) ≤1.
If µA (u)=0, means the element does not belong to the set A
and µA (u)=1 means the element completely belongs to the
fuzzy set A and µA (u)=0.5 is the greatest uncertainty point. In
some cases a definition of µA (u) is given instead of discrete
values is called characteristics functions or membership functions.

4 CONCEPTUAL DATA MODELING
ORIENTED DATABASES

IN

FUZZY OBJECT

Conceptual data modeling is the basic step in the design of
any database. It is a modeling technique to get the conceptual
scheme for the data required by a user. This conceptual
scheme includes the representation of interrelationship existing among data, kinds of entities involved and aggregation,

associations and other related issues. A high level data model
is required to express information without including implementation details. Using such type of schemes leads to enhancement the communication to the non-technical users.
There may be several kinds of uncertainty happening in such
modeling like imprecise attribute, relationships and in the
type of uncertainty. These uncertainties can be handled by
using fuzzy techniques. Different approaches developed for
the purpose of conceptual modeling are discussed in this section.
A methodology has been proposed to transform an EER
model to an OMT model for the purpose of OODB design in
[3]. A schema translation procedure and mapping rules are
well proposed.
Attribute imprecision values as well as fuzzy set of objects
and different uncertainty issues are modeled in a unified
manner using a semantic data model in [4].
Several major ER/EER concepts are fuzzified to conceptually model the imprecise and uncertain data in [5]. Fuzzy extensions to subclass/ super class, generalization/specialization
and shared sub class / category has been discussed. Attribute
inheritance, multiple inheritance and selective inheritances
and inheritance for derived attributes are discussed and introduced in fuzzy context.
The object oriented representation of uncertain and complex information has been proposed using ExIFO2, an extension of IFO data model [6]. Also, different graphical notions
for fuzzy, incomplete and atomic types, complex types, function types and ISA links has been introduced.
A constructive approach using ExIFO to model complex
and uncertain information conceptually and then transformation of the ExIFO into NF2 Logical Data Model has been proposed with the help of algorithms in [7].
An existing IFO data model [8, 9] has been extended to
model fuzziness at different levels in [10]. The new model is
titled as IF2O. Fuzzy printable types, fuzzy abstract and free
types, fuzzy constructs, fuzzy fragments and fuzzy ISA relationships are discussed here in this study.
A system for expressing flexible constraints, which can be
used in the conceptual modeling using enhanced entity relationship, has been introduced in [11,12]. The restrictions have
been proposed using fuzzy quantifiers. In this study, fuzzy

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International Journal of Scientific & Engineering Research, Volume 2, Issue 11, November-2011
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participation constraint, fuzzy cardinality constraints, and
fuzzy completeness constraint in the representation of specializations and fuzzy cardinality constraints in overlapping specializations are proposed. Also, it has studied the fuzzy (min,
max) notation.
A fuzzy extended entity relationship model has been proposed in [13] to deal with inexact information. Also, a formal
framework for mapping a fuzzy extended entity relationship
model to fuzzy object oriented database schema has been provided.
Several points of fuzziness have been identified in UML
class diagram to model and represent inexact information in
[14]. Fuzzy class generalization, aggregation and dependency
have been discussed here.
Classical database models at conceptual and logical level
lacks the rules and semantics to represent such information.
To model such type of information, different classical database
models, like ER/EER, IDEF1X, UML, EXPRESS-G are extended using fuzzy logic, a theory of uncertainty handling.
The fuzzy extensions of these models are proposed in [15].
Also, a SDAI implementation of the object oriented database
and Fuzzy EXPRESS implementation of Fuzzy Object
Oriented Database has been proposed in [15].
The fuzzy extension of XML to model information imprecision has been proposed in [16].
A fuzzy EER model has been discussed in [17]. Several issues like, imprecise attributes, fuzzy entity, fuzzy relationship
and specialization with fuzzy degree have been discussed also.
formal approach for mapping a Fuzzy IFO (IF 2O) model to
a fuzzy object oriented database schema has been proposed in

[18]. Also, a generic fuzzy object oriented database system has
been developed by extending the objects, classes, their relationships, subtype/super type and multiple inheritances in
fuzzy environment.
A pragmatic model has been transformed to the Fuzzy Petri
Net formal models in [19]. Different aspects of behavioral and
structural modeling are also presented in this study.

5 PROPOSED FUZZY OBJECT ORIENTED DATABASE
MODELS

Different object oriented database models have been extended
with fuzzy techniques to handle information inexactness.
These database models include ODMG based object model,
semantic database model, graph based data model, intelligent
database models, rough set and UFO based data models. Also,
object based algebra and many prototypes have been proposed and implemented.

5.1 ODMG based framework
The syntactic and semantic extensions to the ODMG object
model are proposed in [20] in order to deal with fuzzy objects
and related issues. As far as, FODMG is concerned, it has been
formed as a joint international collaborative research effort
among fuzzy database researchers in order to establish common terminology and concepts, to formalize and integrate the
current research in the field of Fuzzy Object Oriented Database.
To incorporate uncertainty with object oriented databases, a

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formal framework has been proposed by Tre, Caluwe and
Cruyssen in [21]. This framework was basically developed by

integrating different aspects from Object Oriented Databases
under ODMG de facto standard and a constraint based algebraic theory.

5.2 Fuzzy semantic database models
An expression of the semantic proximity and evaluated method of the fuzzy association degree has been proposed in [22].
The reasonability and effectiveness has been also derived.
A new database model, FSM (Fuzzy Semantic Model) has
been proposed in [23]. This model presents the techniques to
formalize and conceptualize the fuzziness and semantics of
real world within a manner accepted to human reasoning and
perception.
Different uncertainty issues have been handled regarding
Fuzzy Semantic Model in [24]. Also, first results of an implementation at automotive company PSA Peugeot Citron are
also discussed in this paper.
Conceptual design and different implementation issues has
been discussed and proposed in [25] for fuzzy semantic model. A formal approach is also described to map FSM-based
model to a fuzzy relational object database model.
A fuzzy semantic model has been proposed in [26] to
represent and model fuzziness and uncertainty at different
levels of object oriented modeling. Also, a FSM schema and a
query language adapted to FSM based database have been
introduced.
5.3 Fuzzy graph based models
A Fuzzy Object Oriented Data model (FOOD) is proposed in
[27] by generalizing the graph based data model, so that information inexactness can be handled at different levels. This
proposed model visually represents fuzzy objects and relations. Fuzzy domain of attributes, fuzzy reference relation,
fuzzy instance of relation and fuzzy ISA relations are well explained and represented to produce this model.
The definition of graph based operations to select and
browse a fuzzy object oriented database has been proposed in
[28]. Also, the evaluation mechanism of graph based operations is formalized in terms of graph transformations and

fuzzy pattern matching.
5.4 Intelligent Fuzzy Object Oriented Database models
A fuzzy object oriented approach regarding knowledge representation is discussed in [29]. It is based on the approach of
computing with words. Also, a study on the multimedia system KOOFI (Knowledge based Object Oriented Fuzzy Interface) has been given.
A modeling framework has been introduced in [30], for the
design of complex and knowledge intensive applications. This
approach includes handling the fuzziness at attribute, object/class and class/super class levels, class/class relationship
and other various associations among classes. Logical rules are
designed to define some of the crisp/fuzzy relationships and
associations.
A combination of deductive and object oriented data modeling techniques result in a powerful data modeling tool for
new age knowledge based systems. Complex objects and the
uncertain relationship among then can be well represented by

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International Journal of Scientific & Engineering Research, Volume 2, Issue 11, November-2011
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this new modeling technique. A formal model in this regard
has been implemented and derived in [31]. The prototype for
this model is implemented in Prolog environment. Fuzziness
is considered at attribute, object/class and subclass/class levels.
In [32], a deductive fuzzy object oriented and probabilistic
framework has been developed that provides a formal basis
for the design and implementation of FRIL++, which is an
object oriented extension of FRIL and is a logic programming
language dealing with both fuzziness and probability concepts. Default probabilistic logic rule and probabilistic default

reasoning on fuzzy events are also proposed.
Next generation information systems are considered as the
integration of database and knowledge base technologies. A
fuzzy intelligent Object Oriented Database Architecture has
been proposed in [33]. This model supports flexible modeling
and querying of complex data and knowledge. This IFOOD
architecture is based on the integration of Fuzzy Object
Oriented Database system with a Fuzzy Knowledge Base
(FKB). IFOOD Language, Fuzzy Inference method, Fuzzy Inference Engine Model are discussed. This model is implemented
using C Language Integrated Production System (CLIPS) for
the implementation of object oriented database component.
A new approach in [34] has been developed for modeling
applications, by integrating the approaches of fuzzy, active
and deductive rules. This approach enables objects to perceive
dynamic occurrences and answer user queries, resulting the
production of new knowledge and maintain themselves in a
consistent, stable and up-to-date state. The development of
such an approach is the advancement in the field of knowledge intensive applications requiring intelligent environment.

5.5 Application specific data models
Fuzzy object oriented databases are tested as much suitable to
represent and manipulate the spatial data. The work done in
[35] is the expansion of work proposed in [36]. It is well discussed in the paper that we can incorporate all collection types
described in ODMG de facto standard in this framework.
In [37], the advantages of using fuzzy object data model for
geographic information systems has been discussed. Overview of the model and current implementations of prototype
are also discussed in this study.
An approach for imprecision and uncertainty handling in
images has been introduced in [38]. An object oriented graph
theoretic approach for representing image in the context of

spatial and topological relations existing among object has
been proposed. The assessment of similarity between images
has been performed using fuzzy graph matching.
A fuzzy object oriented framework has been described in
[39] to efficiently model the spatial data. Also, a prototype
system FOOSBALL has been derived to implement this
framework. This prototype system supports both Boolean and
fuzzy queries, represents uncertain query results and also
stores the objects with the uncertain boundaries.
A fuzzy object oriented database model has been proposed
in [40] for the imperfect spatial information based on the fuzzy
set theory and possibility theory.
A fuzzy entity relationship diagram (ERD) data model has
been proposed in [41]. New methods including, object model
flattening, entity payload data containerization, and a non-

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integrated object model design has been proposed for ERD.
A model have been developed to handle different types of
data formats as a single logical entity , based on the concept of
aggregating data into sets in [42]. It also manages the descriptive information. Initially, it was annotated as entity relation
diagram.
The imprecision and uncertainty has been modeled with
spatial data in GIS Applications in [43].
Recently, a fuzzy conceptual data model has been proposed
to represent semantic content of video data in [44]. An intelligent fuzzy object oriented data model for video applications
has been proposed, which supports various flexible queries
including fuzzy semantic, temporal and fuzzy spatial queries.

5.6 Implemented prototypes
A FOODB prototype have been implemented with a data manipulation language based on Encore Query Algebra written
in AKCL (Austin Kyoto Common Lisp), running on Unix operating system in [45].
A FOOD (Fuzzy Object Oriented Database) version of SQL
(Structured Query Language) and a supporting Data Manipulation Language has been designed and implemented by
Umano et. al. in [46].
In [47], a prototype is implemented in the Visual C++ Programming Language and interfacing with the commercial
ODBMS by VERSANT. It has the capability to visually create
fuzzy linguistic terms and use them for object attribute values.
The capability to reason with fuzzy-attribute-valued-objects is
provided through integration with the fuzzy CLIPS Expert
Systems.
To represent imperfections and uncertainty in knowledge
bases, a fuzzy object oriented model has been proposed using
extended Java in [48]. This extended Java permits to model the
fuzzy inheritance. The NCR Fuzzy JLibrary has been used to
deal with information inexactness in class attributes. Also, a
semantic & fuzzy object-oriented data model in Java has been
proposed and implemented called Fuzzy Java, supporting
mono-valued and multi-valued attributes.
Object Relational Database Management Systems
(ORDBMS) is the integrated approach of object oriented methods over relational databases. A new object relational
framework pg4DB has been presented in [49] that enables the
storage and manipulation of fuzzy objects in an object relational system, such as PostgreSQL. Also, it is shown in this
framework that management of fuzzy object oriented data in
object relational systems can be done in transparent way. This
framework allows the user to define a hierarchy of classes to
manage fuzzily described objects and manipulate them using
object relational SQL compliant sentences. This pg4DB is built
over PostgreSQL.

A general framework for managing fuzziness in the conventional object oriented systems has been proposed in [50].
FOODBI, which is a fuzzy object oriented database interface, is
presented as a prototype that generates fuzzy object oriented
schemata. It can be translated into sets of standard java
classes.
In this [51], an extension of proposed FOOD model by
George [73] has been developed. Also, software architecture as
well as a prototype implementation by EXODUS Storage
Manager (ESM) has been discussed for the above model.

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5.7 Rough set based models
A formal introduction and definition of a fuzzy rough object
oriented data base model is presented in [52]. This model is
based on an algebraic type system and a formally defined
constraints. Such data model is very useful in representing
spatial data entities and in their relationship existing among
them.
An approach for integrating the uncertainty in database has
been processed in [53] using indiscernibility relation and approximation region of rough set theory.

tion and fuzzy types are discussed in this proposal.

In [64], an approach of fuzzy object oriented database modeling has been sketched based on level-2 fuzzy sets. In this,
main considerations are at structural and behavioral aspects of
the data and level-2 fuzzy sets are used to generalize the concept ‗type‘.
The model proposed in [65], introduces the concept of
fuzzy type, where properties are ranked in different levels of
precision according to their relationship with type.
The architecture of the prototype implementation of the
model was presented in [66] using Java.

5.8 UFO based models
Generalized fuzzy sets are used to introduce the uncertainty in
fuzzy object oriented data model in [54].
UFO database model has been proposed in [55] that provide semantic capability to enhance object oriented model to
support information imprecision. Such information imprecision is handled by possibility distributions and modeled by
using the concept of role objects. These role objects model imprecise information as well as imprecise roles played by different roles.
A meaning full way of fuzzyfying the inheritance relationship in UFO data model has been discussed in [56].

5.11 Fuzzy object centered models
A mathematical model has been introduced in [67], derived by
the extension principle and fuzzy virtual object concepts. The
fuzzy virtual objects can be considered as the universal objects
in space, time and function to deal with crisp and linguistic
information, simultaneously and consistently. Also, a hypothetical device has been introduced to convert the exact information into linguistic format. These fuzzy objects are much
suitable in multimedia databases to easily understand the linguistic information, like, ―red‘, ―large‖, ―right bottom‖ etc.
In [68], a new object oriented modeling technique has been
developed based on fuzzy theory. Some of the advancements
included in this approach are: extension of class by grouping
objects with similar properties into a fuzzy class, encapsulation of fuzzy rules in classes, evaluating the membership function of a fuzzy class and modeling of uncertain fuzzy associations among classes.
A set of operators has been introduced in [69] to find the
similarity between two objects in a fuzzy environment. A generalized resemblance degree has been proposed between

fuzzy sets of the imprecise objects.
The fuzzification of objects with knowledge base and inference engine has been proposed in [70]. Such objects are considered as intelligent objects. Fuzzy object attributes, relationships, fuzzy generalization and aggregation are formulated in
this framework.
Rossazza et. al. have been proposed a model in [71], in
which all the information is contained in objects. Concepts of
class, class hierarchies and attributes are explained and fuzzy
ranges of allowed values and typical values are specified for
attributes. Graded inclusion relations between classes are also
defined.
An object oriented model has been proposed in [72], and
fuzziness is defined in both structural and behavioral aspects,
at the levels of instantiation, inheritance, relationship among
classes.

5.9 General survey discussions
Different approaches, based on querying and modeling the
fuzzy databases have been reviewed in [57], under category of
crisp database with fuzzy data querying and representation,
and fuzzy database with fuzzy data. Also a comparative study
between fuzzy relational database and fuzzy object oriented
database has been derived in this study.
A good comparison between relational model and object
oriented fuzzy database model has been derived in [58], based
on different modeling and querying issues.
A survey of current approaches on the integration of object
oriented theory and fuzzy techniques have been studied in
[59]. These approaches are categorized under three sub areas,
databases, software engineering and knowledge representation in AI systems.
Different fuzzy database models including object oriented
data models have been reviewed and discussed in [60]. Different concepts of modeling, querying, and data processing are

presented in this study.
5.10 Proposals based on fuzzy type
A framework for the behavioral analysis of the model is presented in [61]. The analysis of the dynamic behavior of the
model through the use of Type I and Type II models is discussed in this framework.
The representation of fuzzy types in a traditional ODBMS
has been discussed in [62]. Also, the implementation of instantiation and inheritance mechanism has been introduced. Fuzzy
types are considered as an important approach for managing
the fuzzy structures.
A proposal of describing different types of fuzziness at different levels in traditional ODBMS has been introduced in
[63]. Imprecise attribute domains, uncertainty in attribute values, uncertain object relationship, fuzzy sub-classes, fuzzy
categories, uncertain object definition, uncertain class defini-

5.12 Proposals based on mathematical fuzzy object
algebra
Fuzzy association algebra (FA algebra) has been discussed in
[73] as a fuzzy algebra for fuzzy object oriented data model (Fmodel) in the context of new intelligent information systems.
Fuzzy objects and the fuzzy associations are uniformly
represented by fuzzy association patterns.
Another framework has been proposed in [74] for modeling
uncertainty in the OODM (Object Oriented Data Model). Calculating membership values or similarity based relations are
the two different approaches to deal with uncertainty. The

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framework combines the two approaches and demonstrated

how these two can be used in conjunction in the OODB. Fuzzy
object algebra is developed in [74]. Two operators have been
defined as an extension to relational algebra, Conjunctive Nest
(CNest) and its collary UnNest. A new operation is also introduced that merges objects at the schema level, called disjunctive nest (DNest.).
Object algebra for manipulating complex objects in fuzzy
object oriented database systems has been proposed in [75]. A
framework has been presented by executing set theoretic operations, like union, intersection, difference on the class construct. Also, inheritance property characteristics for the derived class with fuzzy objects have been discussed.
A mathematical framework for Fuzzy object oriented database, including definition of different constraints, constraint
systems, database schemes, database model, operators, has
been developed in [76]. Different types of generalization constraints, equality constraints, possibilistic constraints, veristic
constraints are included in this algebraic type framework.
An extension of EQUAL-algebra for handling imprecision
is proposed in [77]. EQUAL algebra is the part of object
oriented database model, Extensible and Natural Common
Object Resource (ENCORE) [78].

5.13 Proposals based on hierarchical relationship
An approach for uncertainty modeling in class hierarchies has
been proposed in [79]. Multiple inheritances in class hierarchies has been defined and explained in this approach. Membership degree calculation shows the degree of fuzziness existing in the data values and the semantics of the situation to be
modeled.
In [80], nearest rule has been incorporated with fuzzy object
oriented databases, fuzzy information in the multiple inheritances is retrieved using closeness function and nearest rule.
The use of these techniques also beneficial in the development
of a query language supporting fuzziness to get the answer by
measuring the distance between the query and answer. Also,
two algorithms are provided to implement the nearest rule of
a closeness functions.
In some cases, it may be possible that a subclass may contradict in some way one of its superclass definitions and resulting in an imprecision with super class and subclass relationship. A language feature is presented in [81] to allow class
definitions, which contradicts aspects of other classes.
In [82], a method of computing the default value for unknown objects‘ attribute is proposed. It is based on both association of typical values with the attributes in the intentional

definition of a class and the application of a prioritized aggregation operator to combine typical values appearing in an inheritance structure. This method is also applicable to refine
vague attribute values expressed by means of the fuzzy sets
interpreted as possibility distributions. A new interpretation
of partial inheritance is also proposed, developing the concept
of partial overriding of typical values.
A logic based fuzzy object oriented database model has
been introduced in [83] and a probabilistic default reasoning
approach is given to deal with uncertain inheritance and recognition problems. This proposed approach is also implemented with FRIL++, which is an uncertain and fuzzy object
oriented logic programming language to be used for develop-

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ing intelligent systems.
An object oriented framework has been proposed in [84].
This framework supports a range of allowed values and typical values for the attributes describing a fuzzy class. Different
inclusion relations between classes are also defined. Inheritance mechanisms with different reasoning tasks are also discussed.
A frame-based data structure has been introduced to
represent knowledge in [85]. Inheritance of information from
different frames and inference in inheritance network is also
introduced. A Prioritized Conjunction (PC) operator has been
investigated to combine information contained in frames connected by means of inheritance structure.

5.14 Similarity based approach
Concept of similarity based relation has been used for the derivation to generalize the equality to similarity in [86]. This
permits the representation of imprecision in data and inheritance. An object algebra based on the extension of union, difference, product and selection is also introduced.
5.15 Other proposals
In [87, 88] Bordogna et. al. presented prototypical implementation of fuzziness in object oriented databases models. Vague
attributes and uncertain relations are well represented in these
implementations.
An extended fuzzy object oriented data model [89] has been

proposed to model complex objects, based on possibility distribution and semantic measure. Objects, classes and their relationships and multiple inheritances are extended in this proposed data model.
A flexible generalized fuzzy object model has been introduced in [90].
Abstraction principle based suggestions with a review of
proposals for fuzzy object models for incorporating fuzzy
techniques in object modeling has been introduced in [91].
The introduction of the generic classes in incremental design has been proposed in [92]. Incomplete information has
been expressed in object instances with the use of explicit null
values, presenting the incomplete information both at schema
and object instance level in object oriented database.
Different research issues and principles have been discussed in [93], including fuzzy inheritance, fuzzy objects,
fuzzy subtype/super type hierarchy.
In [94], a fuzzy object oriented data model has been extended to cope with modeling and manipulation of uncertain
information in an object oriented environment.
A good work regarding fuzzy object oriented databases has
been discussed in [95]. Different proposals and discussions
related to conceptual data modeling, querying and fuzzy path
dictionary index: a new access technique as well as algebra for
fuzzy object oriented database has been given.
A good collection of discussions on fuzzy object oriented
databases, UFO data model and uncertainty, Fuzzy Association Algebra has been given in [96].
Fuzzy data mining, fuzzy functional dependency, theoretical framework addresses the definition of fuzzy extensions of
relational database modeling; implementation in specific context of Geographical Information Systems has been discussed
in [97].

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An approach of utilizing a design pattern for fuzzy approach in object oriented database systems has been proposed
in [98]. An original pattern has been introduced to give an
easy understandable and general solution, which is not tightly
coupled with any specific database system or programming.
In [99], the admitted values of attributes are linguistic, the
proposed method hinges on the concept of linguistic approximation and computational enhancements stemming from the
theory of fuzzy neural network.
A new object oriented framework has been proposed for
the modeling of time and to extend the traditional temporal
database concepts in [100].
The concept of nuanced value, nuanced domain and fuzzy
thesaurus has been introduced in [101]. A Chomsky grammar
is used to generate the characteristics membership functions of
the thesaurus terms.

6 QUERYING IN FUZZY OBJECT ORIENTED DATABASES
Querying in databases can be performed by using many languages, like SQL (Structured Query Language) in Relational
Databases, OQL (Object Query Language) in object oriented
databases. But, these traditional database querying techniques
does not support information inexactness. These techniques
are extended by including fuzzy preferences and/or fuzzy
conditions in querying to retrieve the inexact information.
A high level domain independent query language for pictorial and alphanumeric database management, called PICQUERY+ has been introduced in [102]. Certain advancements,
like convenient specification of the data domain space among
a multimedia database federation, visualization of underlying
data models, knowledge based hierarchies and domain rules
are sketched in this paper. Also, the proposed language is illustrated using examples drawn from the medical imaging domain.
The fuzzy query approach has been discussed in [103] for
GIS user interface to deal with natural language. A fuzzy formulae and a prototype for implementing this approach with

sample queries has been discussed.
An extended fuzzy association algebra has been introduced
in [104] based on fuzzy association patterns. It has processed
the fuzzy queries with fuzzy values and linguistic hedges.
An approach has been proposed to obtain approximate answers for NULL queries on similarity relation based fuzzy
object oriented data model in [105]. It is an approach by the
generalization of the former models of analogy.
Different issues regarding the uncertainty modeling and
querying of imperfect spatial information have been discussed
in [106] with reference to object oriented database systems.
A fuzzy Object Query Language has been presented in
[107]. This language supports fuzzy values and fuzzy collections required for image database. Also, it can be used for defining schemas and high level concepts and querying image
databases. This is an extension of the ODMG-OQL language.
Querying issues in multimedia databases as well as comparison of semi structured documents are well introduced in
[108]. A preliminary investigation of fuzzy logic in multimedia
databases is also discussed.
A formal framework of the generalized object oriented
model has been presented in [109]. This model is based on the

7

generalized algebraic type system and constraint system. Also,
object algebra is defined with data manipulation and data definition language.
A new environment for flexible modeling and querying of
complex data and knowledge with uncertainty has been discussed in [110]. An intelligent retrieval of information from
knowledge intensive applications have been proposed based
on a fuzzy knowledge base coupled with fuzzy object oriented
databases.

7 INDEXING IN FUZZY OBJECT ORIENTED DATABASES

Index structures are responsible for efficient and fast access to
data by content. Several indexing techniques have been developed for object oriented databases, like nested inherited index
and enhanced nested inherited structure [111], [112], path index [113]. These index structures are not capable to deal with
imprecise and uncertain data in proposed FOOD model.
Numerous methods have been introduced in [114], for the
indexing of fuzzy sets in databases to improve the performance of querying. These methods are based on rely or inverted files or super-imposed coding.
An overview of different indexing techniques for Fuzzy
Object Oriented Database has been discussed in [115].
A new index structure for supporting different kinds of
fuzziness in FOOD databases and multidimensional indexing,
have been proposed in [116].
Yazici et. al. in [117] has been proposed a new index structure called Food Index (FI) as an extension of the work in
[116]. This supports and deals with different kind of fuzziness
as well as multidimensional indexing. It is also shown that
how FI supports flexible querying and evaluate the performance for exact, range and fuzzy queries. Also, the insertion,
deletion and retrieval algorithms are investigated in this paper.

8 CONCLUSION
Reasoning inexact information extensively exists in data and
knowledge intensive applications and fuzzy techniques plays
vital role to handle such type of information in modeling at
conceptual and logical level, query and data processing, indexing and implementations of the next generation database
systems. Fuzzy object oriented data bases are the natural fit for
many engineering and scientific applications suffering from
the representation and manipulation of inexact information
precisely. A brief overview of different advancements in fuzzy
object oriented databases has been discussed in this paper.
Different conceptual models based on object oriented, EER,
IFO models have been introduced. Numerous approaches for
querying and indexing are also surveyed in this study. These

various issues related to Fuzzy Object Oriented Databases are
listed in the following table I.
Table I Different Issues in Fuzzy Object Oriented Databases
S.
No.
1

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Category

Focus

Conceptual Database Models

Object Oriented and
EER based models

References
[3]-[19]


International Journal of Scientific & Engineering Research, Volume 2, Issue 11, November-2011
ISSN 2229-5518

2

3

4

Proposed Fuzzy
Object Oriented
Database Models

Querying
Fuzzy
Oriented
bases
Indexing
Fuzzy
Oriented
bases

in
Object
Datain
Object
Data-

ExIFO and NF2 based
models
IFO and IF2O Based
Models
XML based models
ODMG based models
Semantic
Database
Models

Graph based models
Intelligent Fuzzy Object Oriented Database Models
Application Specific
Implemented Prototypes
Rough set based
UFO based
General survey discussions
Fuzzy type based
Fuzzy Object Centred
Models
Mathematical Fuzzy
Object Algebra based
Proposal based hierarchical relationship
Similarity
based
models
Fuzzy Object Query
Langugae
(FOQL),
PICQuery

[7]

FOOD Index

[111]-[117]

[8]

[8]-[18]

[9]

[16]
[20, 21]
[22]-[26]

[10]

[27,28]
[29]-[34]

[11]

[35]-[44]
[45]-[51]

[12]

[52, 53]
[54]-[56]
[57]-[60]
[61]-[66]
[67]-[72]
[73]-[78]

[13]

[14]

[15]

[79]-[85]
[16]

[86]
[102]-[110]

[17]

[18]

[19]

[20]

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International Journal of Scientific & Engineering Research, Volume 2, Issue 11, November-2011
ISSN 2229-5518
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